It is important to note that the colimit of eq:thh bicat is evaluated in the \((2,1)\) -category \({C}\mathrm {at}\) , which differs from the 1-categorical colimit in the category of categories, but rather corresponds to the pseudocolimit [1]}. Computing general pseudocolimits can be quite challenging, although there certain helpful methods via weighted colimits of enriched categories [2]} and homotopy colimits of model categories [3]}. The example below illustrates the challenges that arise even in simple examples.
